Here is the full list of all 13 Pure Chess trophies - there are 9 bronze, 3 silver and 1 gold.
Solve 100 mate problems.
Achieve an ELO of 2500 or a Grandmaster Pure Chess rating.
Win a game online.
Deliver checkmate where the king is blocked on both sides by his own rooks.
Perform an En Passant during any full game.
Win an exhibition game against the computer.
Deliver a check by two pieces at the same time.
Put an opponent in check in an exhibition game.
Complete Tournament mode on all three difficulties.
Capture 100 pieces.
Perform a castling move on the queenside during any full game.
Advance a pawn to the eighth rank in an offline game.
Complete all the tutorials.